Field of the Invention
The present invention relates to a system and method for processing NMR (nuclear magnetic resonance) signals and, more particularly, to a system and method for estimating plural signal components contained in an NMR signal by the use of a mathematical model.
Description of Related Art
Nuclear magnetic resonance spectroscopy generally involves detecting a free induction decay (FID) signal emanating as an NMR signal from nuclei under observation within a compound, Fourier transforming the detected FID signal, and creating an NMR spectrum. Based on the spectrum, the molecular structure of the compound is analyzed. In recent years, a system for making a quantitative analysis by utilizing NMR has been put into practical use. This technique is known as quantitative NMR (qNMR). In qNMR, the amount or concentration of a certain substance contained in a sample is found from the intensity (signal intensity) of a peak of interest within a spectrum to be analyzed. Therefore, it is quite important to accurately find the intensity in qNMR. The following methods have been heretofore known as methods of finding intensities. Generally, in qNMR, subjects whose qualitative nature is known to some extent are analyzed and so information about the number and positions of peaks appearing in an NMR spectrum used for analysis is known.
A first method is known as the integration method. In this method, a frequency range containing a peak of interest is set in a spectrum. Integration is performed within this frequency range to find the intensity of the peak of interest. This intensity is equivalent to the area occupied by the waveform of the peak of interest. In this method, it is difficult to determine the integral range. There is the problem that the computed intensity varies depending on the integral range. Furthermore, there is the problem that, if plural peaks overlap with each other, it is difficult to find intensities precisely.
A second method is a waveform separation method (especially, a curve fitting method). In this method, in approximating or simulating a peak of interest in a spectrum, an optimal value of a parameter (e.g., intensity, linewidth, or frequency) defining the waveform is searched for. In this method, however, depending on the spectral waveform, it is observed that there is a tendency that computational results depend on the initial value of the parameter. That is, if the initial value is different, different computational results will occur.
A third method consists of introducing a mathematical model representing a time-domain FID signal and estimating a numerical value or a string of numerical values that gives a parameter value contained in the mathematical model. The Prony method is known as one type of this method (see F. Malz, H. Jancke: J. Pharm. Biomed. Anal., 38, 813 (2005)). In this Prony method, it is assumed that an FID signal is composed of plural signal components. The content of a parameter defining each signal component is estimated. Each individual signal component corresponds to one peak in a spectrum. In practice, however, a spectrum contains various components. Furthermore, a spectral waveform is affected by various kinds of processing performed on the FID signal. Accordingly, it has been proposed to apply the Prony method while assuming more signals components than the peaks of interest in the spectrum. This is known as the high-order estimation method (see Santosh Kumar Bharti, Raja Roy; TrAC, 35, 5 (2012)). The use of this method makes it possible to avoid the problem associated with setting of the integral range, the problem being pointed out regarding the first method. In addition, the problem of the dependence on an initial value as pointed out regarding the second method can be avoided. Therefore, it can be definitely said that this third method is a more objective method than the first and second methods.
In the above-described third method, however, estimation results depend on the number of assumed signal components (order). It can be pointed out that there is the problem that if the number of assumed signal components cannot be determined correctly, the estimation accuracy will deteriorate.